Microtruss structures formed by photopolymerization have been described by Jacobsen et al. in “Compression behavior of micro-scale truss structures formed from self-propagating truss elements”, Acta Materialia 55, (2007) 6724-6733, the entire disclosure of which is hereby incorporated herein by reference. One method and system of creating polymer materials with ordered microtruss structures is disclosed by Jacobsen in U.S. Pat. No. 7,382,959, the entire disclosure of which is hereby incorporated herein by reference. Microtruss materials produced by the method and system are further disclosed by Jacobsen in U.S. patent application Ser. No. 11/801,908, the entire disclosure of which is hereby incorporated herein by reference. A polymer material that is exposed to radiation and results in a self-focusing or self-trapping of light by formation of truss elements is also described by Kewitsch et al. in U.S. Pat. No. 6,274,288, the entire disclosure of which is hereby incorporated herein by reference.
As shown in FIG. 1, the known systems for fabricating microtruss structures may include at least one collimated light source 100 selected to produce a collimated light beam 102; a reservoir 104 having a photomonomer 106 adapted to be polymerized by the collimated light beam 102; and a mask 108 having at least one aperture 110 and positioned between the at least one collimated light source 100 and the reservoir 104. The collimated light source 100 is generally a mercury arc lamp configured to produce collimated ultraviolet (UV) light beams at a desired angle. The mask it typically formed on a layer of quartz glass 112. A light boundary 114 exists between the quartz glass 112 and the air, and the quartz glass 112 and the photomonomer 106, due to the differences in index of refraction between the respective media. The at least one aperture 110 is adapted to guide a portion of the collimated light beam 102 into the photomonomer 106 to form the at least one truss element 116 through a portion of a volume of the photomonomer 106. Multiple truss elements can be formed simultaneously from a single collimated light beam 102 that travels along a path from the light source 100, through the mask 108 and the quartz glass 112, and into the reservoir 104 of the photomonomer 106.
The formation of microtruss structures from the known methods, however, has been constrained by an optical phenomenon known as Snell's Law. Snell's Law states that the ratio of the sines of the angles of incidence and refraction is equivalent to the opposite ratio of the indices of refraction. For example, Snell's Law can be represented asn1 sin θ1=n2 sin θ2 where n1 and n2 denote the first and second media and the angles of incidence and refraction are measured with respect to the normal to the interface between the media. A similar application of Snell's Law to a third and fourth media can be represented asn1 sin θ1=n2 sin θ2=n3 sin θ3=n4 sin θ4 
For a given set of indices where n2>n1, there is limiting angle θ2 corresponding to the physical limit for the incoming angle θ1 of 90 degrees (parallel to the interface.) For the case of light passing from air into a quartz glass mask substrate, the indices of 1.0003 and 1.46 respectively, the limiting angle in the glass substrate is 43 degrees as determined by solving for θ2 in the equation n1 sin θ1=n2 sin θ2.
Under Snell's Law, the refracted angle (θ) is greater than the angle of incidence (α), and the truss elements 116 having desirably large refracted angles (θ) cannot be produced through conventional means where the boundary 114 between the air and the quartz glass 112 exists.
With renewed reference to FIG. 1, a practical example with an incident angle (α) of about 68 degrees is shown. The refracted angle (θ) in the quartz glass 112 is about 40 degrees, or only 3 degrees less than the theoretical limit of 43°. Since the faces of the quartz glass 112 are parallel in FIG. 1, the incident angle (α) as the collimated light beam 102 exits the quartz glass 112 is also about 40 degrees. As the collimated light beam 102 proceeds into the photomonomer 106 with an index of about 1.51, the resulting refracted angle (θ) is about 38 degrees
There is a continuing need for a system and method for fabricating radiation-cured structures with truss elements disposed at angles greater than about 45°, and in particular at angles of greater than about 60°, with respect to normal to the refractive boundary surface. Desirably, the system and method enables production of large-angled radiation-cured structure features, including microtruss structures.